Never mind that this never happens.
Never mind that this is the same sort of baseless attack that had been trotted out against homosexuals (almost exclusively gay men) for centuries.
Never mind that the argument tends to be so heavily focused on women and girls that it borders on paternalistic condescention on the one hand and willfull blindness to the analogue happening to boys and men (or perhaps the silence is based around the tacit position that a woman can't sexually harrass boys and men).
Never mind that - unless the room is otherwise empty and the man in question is able to overcome the sole woman in the room - a man entering a women's room will almost certainly be screamed, kicked, hollered, and pushed right back out again.
Never mind and ALL of those points.
Let's focus, instead, on how the argument is so often presented: that there is a male sexual predator that will put on a dress in order to enter a woman's bathroom, and that stopping trans-women from entering women's bathrooms will stop male sexual predators in dresses from entering a woman's bathroom.
One of the problems with hypervigelence for the safety of women from a man-in-a-dress from entering women's restrooms and locker rooms is that it completely FAILS to consider trans-men and the impact that forcing trans men will have on who goes in to women's bathrooms.
The bathroom bills will force trans-men (who can look HYPER-masculine) to use the women's bathrooms. Now, let's stop for a second and think about what this means. Trans-men are people whose birth certificates say "female" but now look really male. If the bathroom bills require people to use the bathroom that matches the sex listed on their birth certificate, then men-who-were-born-female will be using the women's bathroom. And these men can look REALLY masculine, such as Aydian Dowling.
This transman will be forced into women's bathrooms in North Carolina
This guy looks more masculine than I do, since he can apparently grow a far better beard than I can, has more body hair than me, and better muscle development than me. And Aydian Dowling - and all transmen - will be forced to use the women's bathroom, because their birth certificates say "female."
What this means is that people who were born female, but currently look VERY male will be in women's bathrooms, because of the law. Which only serves to INCREASE the presence of masculinity in a women's bathroom, NOT to diminish it.
The imagined male predator is a man-in-a-dress, but what supporters of these bathroom bills ALL seem to forget (or be completely ignorant of) is the simple fact that a trans-man (i.e., a person who was born female and now presents as male and will be forced to use the women's bathroom) will LOOK EXACTY LIKE A MAN.
In other words, bathroom bills will force MORE male-looking individuals into women's bathrooms, thus making it EASIER for a cis-male (i.e., born a man, presents as a man) to enter a women's bathroom, NOT more difficult.
On the flipside, there are a lot of transwomen who look MORE feminine than lots of ciswomen, so if these bills are to stop the "man-in-a-dress" from walking into a women's bathroom (or - supposedly, but never actually stated - a woman-in-slacks from walking into a men's room), then a simple visual assessment is not going to be either enough OR fairly implemented (since a hyperfeminine transwoman is less likely to be stopped at the entrance to the women's bathroom than a comparatively masculine ciswoman).
For example, there are even beauty pageants for transwomen:
Without being told that these were transwomen, I would posit that it would be difficult for most people to say that all have bith certificates that list "male" as the sex.
In (unfortunate) comparison, there have always been women who have been labeled as being "mannish" or (at minimum) "not feminine." And if one were use only visual assessment against a socialized gender norm, then there will definitely be cases in which (A) transwomen (i.e., women born as male) could enter a women's bathroom (in contravention of the law) and (B) ciswomen (i.e., women born as female) would be stoped from entering a women's bathroom (in contravention of the law).
So the only way to competently implement the bill is to require the presentation of one's birth certificate to a gender assessor who will sit at the door to all public bathrooms. In addition, the birth certificates should be notarized in order to ensure legitimacy (since - as we learned from Trump's witchhunt of Obama - almost anyone can create a forged birth certificate). And, to be equally sure, there should be some additional, corroborating, piece of government-issued identification (perhaps something with a photograph and that traces all changes to name, address, and gender that may have taken place since the issuance of the notarized birth certificate) that should be presented.
In other words, in order to fairly execute these bathroom bills and ACTUALLY think about the safety of women and children against imagined sexual predators going into locker rooms and bathrooms under the cover of being trans, one would have to set up a surveillance state to ensure that all the "men-in-dresses" are caught (regardless of how feminine they look) while allowing all women-born-as-female to enter female locker rooms and restrooms (regardless of how unfeminine they look)... which seems to be at terrible odds with the principle of privacy and no "big brother" government surveillance that the GOP so often says that they support...